There exist terephthalic copolyamides based on a 6 unit (for example, 6,6/6,T or 6/6,T or also 6,I/6,T, comprising predominantly 6,T) which have very high melting points, above 300° C. These products are very rigid and their elongation at break is less than 10%, which prevents them from being used in the field of extrusion of pipes. Patent EP 550 314 gives examples of copolyamides-12/6,T. U.S. Pat. No. 3,843,611 discloses copolyamides-12,12/12,T. U.S. Pat. No. 5,708,125 discloses copolyamides-10,6/10,T. None of these prior arts discloses a possible aptitude with regard to ageing. Furthermore, none of these prior arts discloses the need for flexible polyamides. The aim of the present invention is to find polyamides which have resistance to ageing when they are subjected to a high working temperature, while remaining flexible. Such compositions have now been found.